The transport of slaves from the West African Coast to the New World was called the "Middle Passage". This term arose from the triangular trade route traced on every voyage by the slaver (this term could used to mean either the slave ship and/or the captain of the ship). It began at the home port, proceeded to the African Coast, then to the port of market in the Americas, and back again to the home port. It was during the "middle" leg of the journey, from Africa to the market, that the slaves were on board the ship (Spears 66).
The Middle Passage was a tortuous route which many slaves did not survive. The average mortality is impossible to say-- there just is not enough information existing-- but in 1789, the English Privy Council estimated the figure at about twelve and one-half percent (Mannix 123). Of course, the rates varied by the voyage; on some trips, no slaves died (only a few captains were ever this lucky). On others, nearly half died, usually by contracting the same disease in the unhealthy conditions of the holds. There was one disastrous voyage that almost no one survived: the last voyage of the Gloria. Of almost 600 slaves and an unknown number of crewmen, only four of the crew lived to see land again (Spears 74-77). This, however, was an exceptional case... most records show that slave mortality during the Middle Passage was usually somewhere in the range of three to ten percent.
The lower decks of slavers were breeding grounds for all types of viruses, bacteria, and the like. It was extremely rare for a slave captain to reach the port of market without losing a single slave. But rather than catching a physical illness, many captured slaves seemed to simply have given up the will to live. Separated from their families, tribes, and cultures and thrown into the hostile environment where they knew no one, they succumbed to shock and depression and just faded away. The cramped quarters did nothing to help-- "...the space between the decks where the slaves were to be kept during the time the cargo was being accumulated (three to ten months) and while crossing the Atlantic (six to ten weeks) was a room as long and wide as the ship, but only three feet ten inches high...", and they were packed so tightly together that the average space per slave was "but sixteen inches wide by five and a half feet long" (Spears 69).
Considering this, it is a wonder that anyone at all made it alive to the markets. But make it they did-- and slaving became a profitable business.